# Optimization - Calculus

Find the point closest to the line sqroot(X+1) from the point (3,0).

d = [(x - 3) + (y - 0)]^1/2
d = [(x - 3) + (y)]1/2

Do I now substitute in the equation y = sqroot(X+1) and solve?

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1. Yes, and take the derivative and set to zero for the min distance.

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2. You forgot the squares:

d = [(x - 3)^2 + y^2]1/2

It is easier to minimize d^2:

d^2 = (x-3)^2 + y^2

Insert in here y^2 = x+1 and set the derivative of d^2 w.r.t. x equal to zero.

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3. Thanks both of you.

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